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Simplifying 5n2 + -13 = -1n Reorder the terms: -13 + 5n2 = -1n Solving -13 + 5n2 = -1n Solving for variable 'n'. Reorder the terms: -13 + n + 5n2 = -1n + n Combine like terms: -1n + n = 0 -13 + n + 5n2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -2.6 + 0.2n + n2 = 0 Move the constant term to the right: Add '2.6' to each side of the equation. -2.6 + 0.2n + 2.6 + n2 = 0 + 2.6 Reorder the terms: -2.6 + 2.6 + 0.2n + n2 = 0 + 2.6 Combine like terms: -2.6 + 2.6 = 0.0 0.0 + 0.2n + n2 = 0 + 2.6 0.2n + n2 = 0 + 2.6 Combine like terms: 0 + 2.6 = 2.6 0.2n + n2 = 2.6 The n term is n. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.2n + 0.25 + n2 = 2.6 + 0.25 Reorder the terms: 0.25 + 0.2n + n2 = 2.6 + 0.25 Combine like terms: 2.6 + 0.25 = 2.85 0.25 + 0.2n + n2 = 2.85 Factor a perfect square on the left side: (n + 0.5)(n + 0.5) = 2.85 Calculate the square root of the right side: 1.688194302 Break this problem into two subproblems by setting (n + 0.5) equal to 1.688194302 and -1.688194302.Subproblem 1
n + 0.5 = 1.688194302 Simplifying n + 0.5 = 1.688194302 Reorder the terms: 0.5 + n = 1.688194302 Solving 0.5 + n = 1.688194302 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + n = 1.688194302 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + n = 1.688194302 + -0.5 n = 1.688194302 + -0.5 Combine like terms: 1.688194302 + -0.5 = 1.188194302 n = 1.188194302 Simplifying n = 1.188194302Subproblem 2
n + 0.5 = -1.688194302 Simplifying n + 0.5 = -1.688194302 Reorder the terms: 0.5 + n = -1.688194302 Solving 0.5 + n = -1.688194302 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + n = -1.688194302 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + n = -1.688194302 + -0.5 n = -1.688194302 + -0.5 Combine like terms: -1.688194302 + -0.5 = -2.188194302 n = -2.188194302 Simplifying n = -2.188194302Solution
The solution to the problem is based on the solutions from the subproblems. n = {1.188194302, -2.188194302}
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